Since the terms involving \(\Psi _k[\phi ]\)  in (REF ) have the form of a redundant operator, the liberty to choose \(\Psi _k[\phi ]\)  is precisely the liberty to specify the flow of all inessential couplings. Thus, for each inessential coupling we specify an RG condition, understood as a constraint on the form of \(\Gamma _k[\phi ]\)  along the RG flow, then we solve the flow equation under this condition for the beta functions of the essential couplings and gamma functions which parametrise \(\Psi _k[\phi ]\) . Different essential schemes correspond to different sets of RG conditions for the inessential couplings.
From a geometric point of view, we can think of reparameterisations as local frame transformations on configuration space that are analogous to gauge transformations [1]}, [2]}. RG conditions are, therefore, analogous to gauge fixing conditions which fix a particular frame, as with gauge conditions we typically want to find RG conditions that minimise the complexity of a given observable.
